Deformation of Cartan curvature on Finsler manifolds
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2119-2139
Published online August 10, 2017
Printed November 30, 2017
Behroz Bidabad, Alireza Shahi, Mohamad Yar Ahmadi
Amirkabir University of Technology, Amirkabir University of Technology, Amirkabir University of Technology
Abstract : Here, certain Ricci flow for Finsler $n$-manifolds is considered and deformation of Cartan $hh$-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.
Keywords : deformation, Finsler Ricci flow, blow up, evolution, heat-type equation
MSC numbers : 53C60, 53C44
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